Egyptian authorities have arrested the Muslim Brotherhood's main English-language spokesman, state media reported on Tuesday, in a continuation of the military-backed government's crackdown on supporters of ousted Islamist president Mohamed Morsi.

Egypt's army and police have killed up to a thousand of Morsi's supporters since his 3 July overthrow and arrested thousands more in a campaign that polls suggest is supported by the overwhelming majority of Egyptians, who view Morsi's allies as terrorists.

Brotherhood spokesman Gehad el-Haddad, who has spent part of his life in Britain, was the face of the pro-Morsi movement in the international media before his arrest on Tuesday. He is a hate figure for Morsi's opponents, who see him as an embodiment of the way the Brotherhood has, in their view, presented a favourable image to the west but a contradictory hard line to its own supporters.

Officials said Haddad – the son of one of Morsi's closest advisers – is being held on suspicion of incitement to violence, a charge Brotherhood supporters claim is purely political.

Elsewhere, secular activists fear the crackdown on Islamists will soon widen to critics of both the Brotherhood and the army, following a police raid on the offices of the 6 April group – the movement that helped lead the protests that forced the fall of Hosni Mubarak in 2011 – and the arrest of a prominent labour lawyer regarded as a hero of the 2011 uprising.

The campaign against the Brotherhood has also taken place alongside a crackdown on journalists suspected of presenting information unfavourable to the army and its supporters. Ahmed Abu Deraa faces a military trial for his reporting on the army campaign in the Sinai peninsula.

A renowned Canadian film-maker, John Greyson, and his companion, Tarek Loubani, a doctor, have embarked on a hunger strike after they said they were arrested arbitrarily when asking at a police station for directions on 15 August.